Looped Recurrence Proof Audit

This appendix keeps the theorem-card trail for the Looped Recurrence Contracts lesson. The lesson teaches recurrence schedules as finite contracts; this page is for checking the proof families.

These cards certify finite loop budgets, exit certificates, active-token boundaries, block routes, recurrent-state closure, and schedule controls. They do not prove recursive reasoning, semantic convergence, model quality, speed, memory savings, context-length improvement, or deployment behavior.

Recurrence Budget Timeline

Exit Certificate

Token-Level Recurrence

Work-Budget Accounting

Middle-Block And Multi-Resolution Routes

Recurrent-State Prototype

Source Trail

Paper source: Coil Attention And Memory

Lean source: Circle/Applications/CircleAI.lean

Python source: circle_math/applications/circle_ai.py

Back: Looped Recurrence Contracts Next: Physics